\subsection{同分母的分式加减法}\label{subsec:8-6}
\begin{enhancedline}

与同分母的分数加减法类似，\zhongdian{同分母的分式相加减，把分子相加减，分母不变。}用式子表示是：
\begin{center}
    \setlength{\fboxsep}{.6em}
    \framebox{\quad
        $\dfrac{a}{c} \pm \dfrac{b}{c} = \dfrac{a \pm b}{c} \juhao$
        \;}
\end{center}

\liti 计算 $\dfrac{x + 3y}{x^2 - y^2} - \dfrac{x + 2y}{x^2 - y^2} + \dfrac{2x - 3y}{x^2 - y^2}$。

\jie $\begin{aligned}[t]
        & \dfrac{x + 3y}{x^2 - y^2} - \dfrac{x + 2y}{x^2 - y^2} + \dfrac{2x - 3y}{x^2 - y^2} \\
    ={} & \dfrac{(x + 3y) - (x + 2y) + (2x - 3y)}{x^2 - y^2} \\
    ={} & \dfrac{2x - 2y}{x^2 - y^2} = \dfrac{2(x - y)}{(x + y)(x - y)} = \dfrac{2}{x + y} \juhao
\end{aligned}$

\liti 计算 $\dfrac{m + 2n}{n - m} + \dfrac{n}{m - n} - \dfrac{2m}{n - m}$。

\jie $\begin{aligned}[t]
        & \dfrac{m + 2n}{n - m} + \dfrac{n}{m - n} - \dfrac{2m}{n - m} \\
    ={} & \dfrac{m + 2n}{n - m} - \dfrac{n}{n - m} - \dfrac{2m}{n - m} \\
    ={} & \dfrac{m + 2n - n - 2m}{n - m} = \dfrac{n - m}{n - m} = 1 \juhao
\end{aligned}$

\lianxi
\begin{xiaotis}

\xiaoti{计算：}
\begin{xiaoxiaotis}

    \begin{tblr}{columns={18em, colsep=0pt}, rows={rowsep+=.25em}}
        \xxt{$\dfrac{3}{a} + \dfrac{12}{a} - \dfrac{5}{a}$；} & \xxt{$\dfrac{5}{m} - \dfrac{15}{m}$；} \\
        \xxt{$\dfrac{a}{x - y} - \dfrac{a}{x - y}$；} & \xxt{$\dfrac{x}{x + y} + \dfrac{y}{x + y}$。}
    \end{tblr}

\end{xiaoxiaotis}


\xiaoti{计算：}
\begin{xiaoxiaotis}

    \begin{tblr}{columns={18em, colsep=0pt}, rows={rowsep+=.25em}}
        \xxt{$\dfrac{a^2}{a - b} - \dfrac{b^2}{a - b}$；} & \xxt{$\dfrac{2x + 5}{2x + 2} - \dfrac{x - 1}{2x + 2} + \dfrac{2x - 3}{2x + 2}$；} \\
        \xxt{$\dfrac{5x}{y - 3} + \dfrac{2x}{3 - y}$；} & \xxt{$\dfrac{2a}{2a - b} + \dfrac{b}{b - 2a}$；} \\
        \xxt{$\dfrac{a^2 - c^3}{a^2 - b^2} + \dfrac{b^2 - c^3}{b^2 - a^2}$；} & \xxt{$\dfrac{4}{x - 2} + \dfrac{x + 2}{2 - x}$；} \\
        \xxt{$\dfrac{x + 2y}{x^2 - y^2} + \dfrac{y}{y^2 - x^2} - \dfrac{2x}{x^2 - y^2}$。}
    \end{tblr}

\end{xiaoxiaotis}

\end{xiaotis}

\end{enhancedline}

